C₂²×C₇×C₅²⋊C₃ #14523668

order	2100
isoclinism	isoclinic class of C₅²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₇ · Schur multiplier (H₂) = C₂×C₅

Aliases

C₂²×C₇×C₅²⋊C₃

	subgroup	G/H
center, hypercenter	C₂²×C₇	C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂²×C₅²×C₇	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂²×C₇

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 420

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2)(5,6,7,8,9,10,11)(12,13,15)(14,18,20)(16,21,24)(17,23,26)(19,22,25);(3,4)(12,14,19,24,26)(13,18,22,16,17)(15,21,20,23,25)

308 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 148);